Question

if x square plus 1 by x Square equals to 5 then x plus 1 by x equals to ? and x minus 1by x eq
uals to ?​

Answer 1

Step-by-step explanation:

$\frac{ {x}^{2} + 1 }{ {x}^{2} } = 5 \\ {x}^{2} + 1 = 5 {x}^{2} \\ {x}^{2} - 5 {x}^{2} + 1 = 0 \\ - 4 {x}^{2} + 1 = 0 \\ - 4 {x}^{2} = - 1 \\ {x}^{2} = \frac{1}{4} \\ x = + - \sqrt{ \frac{1}{4} } = + - \frac{1}{2} \\ x + \frac{1}{x} = \frac{1}{2} + 2 \\ = \frac{5}{2} \\ and \: \\ = - \frac{1}{2} - 2 \\ = \frac{ - 5}{2} \\ x - \frac{1}{x} = \frac{1}{2} - 2 \\ = \frac{ - 3}{2} \\ and \\ = \frac{ - 1}{2} + 2 \\ = \frac{ 3}{2 } \\ so \\ x + \frac{1}{x } = ( \frac{5}{2} and \frac{ - 5}{2} ) \\ x - \frac{1}{x} = ( \frac{3}{2} and \frac{ - 3}{2} )$